A refreshment stand sells popcorn and soft drinks. Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. 38 students bought both popcorn and a drink.
Are buying a drink and buying popcorn independent or dependent events?
To determine whether buying a drink and buying popcorn are independent or dependent events, we need to compare the probabilities of each event separately and the probability of both events happening together.
Let's start by finding the probability of a student buying popcorn. Since 62 students bought popcorn out of 100, the probability of buying popcorn is 62/100, which simplifies to 31/50.
Next, let's find the probability of a student buying a drink. Since 47 students bought a drink out of 100, the probability of buying a drink is 47/100, which does not simplify.
Now, let's find the probability of a student buying both popcorn and a drink. Since 38 students bought both popcorn and a drink out of 100, the probability of both events happening is 38/100, which can simplify to 19/50.
If buying a drink and buying popcorn were independent events, then the probability of both events happening would be equal to the product of their individual probabilities. Therefore, if:
P(Popcorn) * P(Drink) = P(Popcorn and Drink)
We can test this:
(31/50) * (47/100) = 19/50
By simplifying the left side of the equation, we get:
(31/100) * (47/100) = 19/50
This equation is not true, as the left side does not equal the right side. Therefore, the two events, buying a drink and buying popcorn, are dependent events.